<center>
<b><font size="+2">Entering inequalities</font></b>
</center>

<ul type="square">

<li><u>Types of operators:</u>
<blockquote>
<table border="0" cellspacing="2">
<tr><td><tt>&lt;</tt></td><td>&nbsp;&nbsp;&nbsp; less than</td></tr>
<tr><td><tt>&lt;=</tt></td><td>&nbsp;&nbsp;&nbsp; less than or equal to (&nbsp; <tt>=&lt;</tt> &nbsp; might also work)</td></tr>
<tr><td><tt>=</tt></td><td>&nbsp;&nbsp;&nbsp; equals</td></tr>
<tr><td><tt>!=</tt></td><td>&nbsp;&nbsp;&nbsp; not equal to (uses exclamation point)</td></tr>
<tr><td><tt>&gt;</tt></td><td>&nbsp;&nbsp;&nbsp; greater than</td></tr>
<tr><td><tt>&gt;=</tt></td><td>&nbsp;&nbsp;&nbsp; greater than or equal to (&nbsp; <tt>=&gt;</tt> &nbsp; might also work)</td></tr>
</table>
</blockquote>
</li>

<li><u>Special symbols:</u>
<blockquote>
<tt>infinity</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>inf</tt> &nbsp;&nbsp;means positive infinity<br />
<tt>-infinity</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>-inf</tt> &nbsp;&nbsp;means negative infinity<br />
<tt>R</tt> &nbsp;&nbsp;means all real numbers<br />
<tt>R</tt> &nbsp;&nbsp;is the same as&nbsp;&nbsp; <tt>-inf < x < inf</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>(-inf,inf)</tt><br />
<tt>{2,4,5}</tt> &nbsp;&nbsp;using curly braces denotes a finite set<br /> 
<tt>NONE</tt> &nbsp;&nbsp;or a pair of curly braces&nbsp;&nbsp; <tt>{}</tt> &nbsp;&nbsp;means the empty set<br />
<tt>U</tt> &nbsp;&nbsp;denotes the union of intervals
</blockquote>
</li>

<li><u>Entering answers using inequality or interval notation:</u>
<blockquote>
<table border="1" cellspacing="0" cellpadding="5">
<tr><td>Inequality<br />Notation</td><td><font color="#FF0000">* </font>Interval<br />Notation</td><td>Remarks</td></tr>
<tr><td><tt>x&LT;2</tt></td><td><tt>(-infinity,2)</tt></td>
    <td>Use rounded parentheses <nobr><tt>(</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>)</tt></nobr> at infinite endpoints</td></tr>
<tr><td><tt>x&GT;2</tt></td><td><tt>(2,infinity)</tt></td><td>&nbsp;</td></tr>
<tr><td><tt>x&LT;=2</tt></td><td><tt>(-infinity,2]</tt></td><td>&nbsp;</td></tr>
<tr><td><tt>x&GT;=2</tt></td><td><tt>[2,infinity)</tt></td><td>&nbsp;</td></tr>
<tr><td><tt>0&LT;x&LT;=2</tt></td><td><tt>(0,2]</tt></td><td>&nbsp;</td></tr>
<tr><td><nobr><tt>0&LT;x and x&LT;2</tt></nobr></td><td><tt>(0,2)</tt></td>
    <td><tt>and</tt> &nbsp;&nbsp;is special</td></tr>
<tr><td><nobr><tt>x&LT;0 or x&GT;2</tt></nobr></td><td><tt>(-inf,0)U(2,inf)</tt></td>
    <td><tt>or</tt> &nbsp;&nbsp;is special<br /><tt>U</tt> &nbsp;&nbsp;denotes union</td></tr>
<tr><td><nobr><tt>x=0 or x=2</tt></nobr></td><td><tt>{0,2}</tt></td>
    <td>finite sets are allowed using curly braces&nbsp;&nbsp; <tt>{a,b,c}</tt></td></tr>
<tr><td><nobr><tt>x<3 or x>3</tt></nobr></td><td><tt>(-inf,3)U(3,inf)</tt><br /><tt>x != 3</tt><br /><tt>R-{3}</tt></td><td>set differences are allowed</td></tr>
</table>
<br />
<font color="#FF0000">* Some questions may not allow interval notation to be used</font>
</blockquote>
</li>

<li><u>Tips for entering inequalities and intervals:</u>
<blockquote>
If an interval includes an endpoint, use square brackets: <nobr><tt>[</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>]</tt></nobr><br /><br />
If an interval excludes an endpoint or an endpoint is infinite, use rounded parentheses: <nobr><tt>(</tt> &nbsp;&nbsp;or&nbsp;&nbsp; <tt>)</tt></nobr><br /><br />
Use curly braces to enclose finite sets and commas to separate elements the set: <nobr><tt>{ -3, pi, 2/5, 0.75 }</tt></nobr><br /><br />
All sets should be expressed in their simplest form in interval notation with no overlapping intervals.  For example,&nbsp;&nbsp; <tt>[2,4]U[3,5]</tt> &nbsp;&nbsp;is not equivalent to&nbsp;&nbsp; <tt>[2,5]</tt></br /><br />
If you are asked to find the range of a function <tt>y = f(x)</tt>, your inequality should be in terms of the variable <tt>y</tt>
</blockquote>
</li>

</ul>
